Monocular re-localization enables robots to estimate camera poses from visual observations. However, many existing methods rely on dense maps or large reference image databases, which face scalability limitations and privacy risks. OpenStreetMap (OSM), as a lightweight privacy-preserving map, offers semantic and geometric information with global scalability. Nonetheless, OSM localization remains challenging due to cross-modal discrepancies between natural images and OSM, as well as the high cost of global map-based localization. In this paper, we propose an uncertainty-aware hierarchical search framework with semantic alignment for localization in OSM. First, object-centric DINO-ViT tokens are exploited to reduce the semantic gap between ground-view observations and OSM vectors. Second, global dense matching is decomposed into coarse FFT correlation and uncertainty-controlled local refinement. Extensive experiments demonstrate that our method significantly improves localization accuracy and speed. When trained on a single dataset, the 3$^\circ$ orientation recall of our method even outperforms the 5$^\circ$ recall of state-of-the-art methods.